I said it's "debatable" that they wish to join Pakistan. My opinion that they dont wish to join Pakistan is based on a survey done by a British based research institute funded by Saif Al Gaddafi, Libyan Qaddafis son.
https://www.chathamhouse.org/sites/default/files/public/Research/Asia/0510pp_kashmir.pdf
The reason why India wants to keep Kashmir ?
1. Territorial integrity. It can lead to a bad precedent for India
2. Can't let terrorism/jihadists win. They will feel emboldened world over.
3. Ego
3. Water
5. Tourism Potential
6. India's claim of being a secular nation so a Muslim majority state can be a part of India
7. Historically Hindu place ( check the history behind the name of Kashmir), so Hindus have some sentiments attached, especially Kashmiri Pandits (Right Wingers particularly are sensitive about this).
Yes, it's expensive, yes it leads to death and destruction for both sides, yes it gives India bad press, but it seems worth it for all the above reasons. I personally, am on the fence on it. Rahe saath to accha, na rahe to aur bhi accha.